The simulation box is a cube with edge length \(L\) , the total number of dipoles is \(N\)  and the volume fraction
is \(\Phi =N\pi {}d^3/(6L^3)\) .
We consider periodic boundary conditions by repeating the simulation cubic box identically in the 3 dimensions.
The long range DDI interaction is treated through the Ewald summation technique [1]}, [2]},
with a cut-off \(k_c=8\;k_m\) , \(k_m=(2\pi /L)\) , in the sum of reciprocal space and the \(\alpha \)  parameter of the
direct sum chosen is \(\alpha =5.80\)  [2]}.
The Ewald sums are performed with the so-called
conductive external conditions [1]}, [2]}, i.e. the system is embedded in a medium with
infinite permeability, \(\mu _s=\infty \) , which is a way to avoid the demagnetizing effect and thus
to simulate the intrinsic bulk material properties regardless of the external surface and system
shape effects.
